1 Evaluate without using a calculator: $$ 11 \sqrt[4]{10000} $$ $$ 1.2 \sqrt[3]{64^{2}} $$ $$ 13 \sqrt[4]{16^{3}} $$ $$ 1.4(0,125)^{-\frac{2}{3}} $$ $$ 1.5\left(2 \frac{14}{25}\right)^{-\frac{1}{2}} $$ $$ 1.6\left(1 \frac{11}{25}\right)^{-\frac{1}{2}} $$ $$ 1.7 \quad(-2)^{0}+\sqrt[3]{8}+\left(\sqrt{3}\right)^{2} $$ $$ 1.8(0,0625)^{-\frac{1}{4}} $$ $$ 7.9(0,064)^{\frac{2}{3}} $$ $$ 1.10 \quad 81^{-\frac{3}{4}}\left(27^{\frac{2}{3}}-9^{\frac{3}{2}}\right) $$ $$ 1.1149^{-\frac{1}{2}}\left(125^{\frac{2}{3}}-9^{0}\right) $$ $$ 1.1216^{\frac{1}{2}}+16^{\frac{3}{4}}-64^{-\frac{1}{3}} $$

Question

UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$11\times 10000^{\frac{1}{4}}$$
- step1: Evaluate the power:
  $$11\times 10$$
- step2: Multiply:
  $$110$$
Calculate or simplify the expression $$ (-2)^0 + (8)^(1/3) + (3)^(2) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(-2\right)^{0}+8^{\frac{1}{3}}+3^{2}$$
- step1: Evaluate the power:
  $$1+8^{\frac{1}{3}}+3^{2}$$
- step2: Evaluate the power:
  $$1+2+3^{2}$$
- step3: Evaluate the power:
  $$1+2+9$$
- step4: Add the numbers:
  $$12$$
Calculate or simplify the expression $$ 13 * (16^3)^(1/4) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$13\left(16^{3}\right)^{\frac{1}{4}}$$
- step1: Multiply the exponents:
  $$13\times 16^{3\times \frac{1}{4}}$$
- step2: Multiply:
  $$13\times 16^{\frac{3}{4}}$$
- step3: Evaluate the power:
  $$13\times 8$$
- step4: Multiply:
  $$104$$
Calculate or simplify the expression $$ (0.0625)^(-1/4) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$0.0625^{\frac{-1}{4}}$$
- step1: Rewrite the fraction:
  $$0.0625^{-\frac{1}{4}}$$
- step2: Convert the expressions:
  $$\left(\frac{1}{16}\right)^{-\frac{1}{4}}$$
- step3: Transform the expression:
  $$16^{\frac{1}{4}}$$
- step4: Factor the number:
  $$\left(2^{4}\right)^{\frac{1}{4}}$$
- step5: Evaluate the power:
  $$2$$
Calculate or simplify the expression $$ 1.2 * (64^2)^(1/3) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$1.2\left(64^{2}\right)^{\frac{1}{3}}$$
- step1: Multiply the exponents:
  $$1.2\times 64^{2\times \frac{1}{3}}$$
- step2: Multiply:
  $$1.2\times 64^{\frac{2}{3}}$$
- step3: Rewrite the expression:
  $$1.2\times 16$$
- step4: Multiply the numbers:
  $$19.2$$
Calculate or simplify the expression $$ 7.9 * (0.064)^(2/3) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$7.9\times 0.064^{\frac{2}{3}}$$
- step1: Convert the expressions:
  $$7.9\left(\frac{8}{125}\right)^{\frac{2}{3}}$$
- step2: Convert the expressions:
  $$\frac{79}{10}\left(\frac{8}{125}\right)^{\frac{2}{3}}$$
- step3: Multiply the numbers:
  $$\frac{158}{125}$$
Calculate or simplify the expression $$ 1.4 * (0.125)^(-2/3) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$1.4\times 0.125^{\frac{-2}{3}}$$
- step1: Rewrite the fraction:
  $$1.4\times 0.125^{-\frac{2}{3}}$$
- step2: Convert the expressions:
  $$1.4\left(\frac{1}{8}\right)^{-\frac{2}{3}}$$
- step3: Rewrite the expression:
  $$1.4\times 4$$
- step4: Multiply the numbers:
  $$5.6$$
Calculate or simplify the expression $$ 81^(-3/4) * (27^(2/3) - 9^(3/2)) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$81^{\frac{-3}{4}}\left(27^{\frac{2}{3}}-9^{\frac{3}{2}}\right)$$
- step1: Subtract the numbers:
  $$81^{\frac{-3}{4}}\left(-18\right)$$
- step2: Rewrite the fraction:
  $$81^{-\frac{3}{4}}\left(-18\right)$$
- step3: Evaluate the power:
  $$\frac{1}{27}\left(-18\right)$$
- step4: Multiply:
  $$-\frac{2}{3}$$
Calculate or simplify the expression $$ 49^(-1/2) * (125^(2/3) - 9^0) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$49^{\frac{-1}{2}}\left(125^{\frac{2}{3}}-9^{0}\right)$$
- step1: Evaluate the power:
  $$49^{\frac{-1}{2}}\left(125^{\frac{2}{3}}-1\right)$$
- step2: Subtract the numbers:
  $$49^{\frac{-1}{2}}\times 24$$
- step3: Rewrite the fraction:
  $$49^{-\frac{1}{2}}\times 24$$
- step4: Evaluate the power:
  $$\frac{1}{7}\times 24$$
- step5: Multiply:
  $$\frac{24}{7}$$
Calculate or simplify the expression $$ 1.6 * (1 + 11/25)^(-1/2) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$1.6\left(1+\frac{11}{25}\right)^{\frac{-1}{2}}$$
- step1: Add the numbers:
  $$1.6\left(\frac{36}{25}\right)^{\frac{-1}{2}}$$
- step2: Rewrite the fraction:
  $$1.6\left(\frac{36}{25}\right)^{-\frac{1}{2}}$$
- step3: Convert the expressions:
  $$\frac{8}{5}\left(\frac{36}{25}\right)^{-\frac{1}{2}}$$
- step4: Multiply the numbers:
  $$\frac{4}{3}$$
Calculate or simplify the expression $$ 16^(1/2) + 16^(3/4) - 64^(-1/3) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$16^{\frac{1}{2}}+16^{\frac{3}{4}}-64^{\frac{-1}{3}}$$
- step1: Rewrite the fraction:
  $$16^{\frac{1}{2}}+16^{\frac{3}{4}}-64^{-\frac{1}{3}}$$
- step2: Evaluate the power:
  $$4+16^{\frac{3}{4}}-64^{-\frac{1}{3}}$$
- step3: Evaluate the power:
  $$4+8-64^{-\frac{1}{3}}$$
- step4: Evaluate the power:
  $$4+8-\frac{1}{4}$$
- step5: Add the numbers:
  $$12-\frac{1}{4}$$
- step6: Reduce fractions to a common denominator:
  $$\frac{12\times 4}{4}-\frac{1}{4}$$
- step7: Transform the expression:
  $$\frac{12\times 4-1}{4}$$
- step8: Multiply the numbers:
  $$\frac{48-1}{4}$$
- step9: Subtract the numbers:
  $$\frac{47}{4}$$
Calculate or simplify the expression $$ 1.5 * (2 + 14/25)^(-1/2) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$1.5\left(2+\frac{14}{25}\right)^{\frac{-1}{2}}$$
- step1: Add the numbers:
  $$1.5\left(\frac{64}{25}\right)^{\frac{-1}{2}}$$
- step2: Rewrite the fraction:
  $$1.5\left(\frac{64}{25}\right)^{-\frac{1}{2}}$$
- step3: Convert the expressions:
  $$\frac{3}{2}\left(\frac{64}{25}\right)^{-\frac{1}{2}}$$
- step4: Multiply the numbers:
  $$\frac{15}{16}$$
Let's evaluate each expression step by step:

1. **Evaluate $$ 11 \sqrt[4]{10000} $$**:
   - First, calculate $$ \sqrt[4]{10000} $$:
     $$
     \sqrt[4]{10000} = (10000)^{1/4} = (10^4)^{1/4} = 10
     $$
   - Now, multiply by 11:
     $$
     11 \times 10 = 110
     $$

2. **Evaluate $$ 1.2 \sqrt[3]{64^{2}} $$**:
   - Calculate $$ \sqrt[3]{64^2} $$:
     $$
     \sqrt[3]{64^2} = (64)^{2/3} = (4^3)^{2/3} = 4^2 = 16
     $$
   - Now, multiply by 1.2:
     $$
     1.2 \times 16 = 19.2
     $$

3. **Evaluate $$ 13 \sqrt[4]{16^{3}} $$**:
   - Calculate $$ \sqrt[4]{16^3} $$:
     $$
     \sqrt[4]{16^3} = (16)^{3/4} = (4^2)^{3/4} = 4^{3/2} = 8
     $$
   - Now, multiply by 13:
     $$
     13 \times 8 = 104
     $$

4. **Evaluate $$ 1.4(0.125)^{-\frac{2}{3}} $$**:
   - Calculate $$ (0.125)^{-\frac{2}{3}} $$:
     $$
     (0.125)^{-\frac{2}{3}} = (1/8)^{-\frac{2}{3}} = 8^{\frac{2}{3}} = (2^3)^{\frac{2}{3}} = 2^2 = 4
     $$
   - Now, multiply by 1.4:
     $$
     1.4 \times 4 = 5.6
     $$

5. **Evaluate $$ 1.5\left(2 \frac{14}{25}\right)^{-\frac{1}{2}} $$**:
   - Convert $$ 2 \frac{14}{25} $$ to an improper fraction:
     $$
     2 \frac{14}{25} = \frac{50 + 14}{25} = \frac{64}{25}
     $$
   - Calculate $$ \left(\frac{64}{25}\right)^{-\frac{1}{2}} $$:
     $$
     \left(\frac{64}{25}\right)^{-\frac{1}{2}} = \frac{25^{1/2}}{64^{1/2}} = \frac{5}{8}
     $$
   - Now, multiply by 1.5:
     $$
     1.5 \times \frac{5}{8} = \frac{7.5}{8} = \frac{15}{16}
     $$

6. **Evaluate $$ 1.6\left(1 \frac{11}{25}\right)^{-\frac{1}{2}} $$**:
   - Convert $$ 1 \frac{11}{25} $$ to an improper fraction:
     $$
     1 \frac{11}{25} = \frac{25 + 11}{25} = \frac{36}{25}
     $$
   - Calculate $$ \left(\frac{36}{25}\right)^{-\frac{1}{2}} $$:
     $$
     \left(\frac{36}{25}\right)^{-\frac{1}{2}} = \frac{25^{1/2}}{36^{1/2}} = \frac{5}{6}
     $$
   - Now, multiply by 1.6:
     $$
     1.6 \times \frac{5}{6} = \frac{8}{3} = 2\frac{2}{3}
     $$

7. **Evaluate $$ (-2)^{0}+\sqrt[3]{8}+\left(\sqrt{3}\right)^{2} $$**:
   - Calculate each term:
     $$
     (-2)^{0} = 1, \quad \sqrt[3]{8} = 2, \quad \left(\sqrt{3}\right)^{2} = 3
     $$
   - Now, sum them:
     $$
     1 + 2 + 3 = 6
     $$

8. **Evaluate $$ (0.0625)^{-\frac{1}{4}} $$**:
   - Calculate $$ (0.0625)^{-\frac{1}{4}} $$:
     $$
     (0.0625)^{-\frac{1}{4}} = (1/16)^{-\frac{1}{4}} = 16^{\frac{1}{4}} = 2
     $$

9. **Evaluate $$ 7.9(0.064)^{\frac{2}{3}} $$**:
   - Calculate $$ (0.064)^{\frac{2}{3}} $$:
     $$
     (0.064)^{\frac{2}{3}} = (1/16)^{\frac{2}{3}} = 16^{-\frac{2}{3}} = \frac{1}{4}
     $$
   - Now, multiply by 7.9:
     $$
     7.9 \times \frac{1}{4} = 1.975
     $$

10. **Evaluate $$ 81^{-\frac{3}{4}}\left(27^{\frac{2}{3}}-9^{\frac{3}{2}}\right) $$**:
    - Calculate each part:
      $$
      81^{-\frac{3}{4}} = (3^4)^{-\frac{3}{4}} = 3^{-3} = \frac{1}{27}
      $$
      $$
      27^{\frac{2}{3}} = (3^3)^{\frac{2}{3}} = 3^2 = 9
      $$
      $$
      9^{\frac{3}{2}} = (3^2)^{\frac{3}{2}} = 3^3 = 27
      $$
    - Now, calculate the expression:
      $$
      9 - 27 = -18
      $$
      $$
      \frac{1}{27} \times (-18) = -\frac{2}{3}
      $$

11. **Evaluate $$ 49^{-\frac{1}{2}}\left(125^{\frac{2}{3}}-9^{0}\right) $$**:
   
Here are the simplified evaluations of each expression: 1. $$ 11 \sqrt[4]{10000} = 110 $$ 2. $$ 1.2 \sqrt[3]{64^{2}} = 19.2 $$ 3. $$ 13 \sqrt[4]{16^{3}} = 104 $$ 4. $$ 1.4(0.125)^{-\frac{2}{3}} = 5.6 $$ 5. $$ 1.5\left(2 \frac{14}{25}\right)^{-\frac{1}{2}} = \frac{15}{16} $$ 6. $$ 1.6\left(1 \frac{11}{25}\right)^{-\frac{1}{2}} = 2\frac{2}{3} $$ 7. $$ (-2)^{0}+\sqrt[3]{8}+\left(\sqrt{3}\right)^{2} = 6 $$ 8. $$ (0.0625)^{-\frac{1}{4}} = 2 $$ 9. $$ 7.9(0.064)^{\frac{2}{3}} = 1.975 $$ 10. $$ 81^{-\frac{3}{4}}\left(27^{\frac{2}{3}}-9^{\frac{3}{2}}\right) = -\frac{2}{3} $$ 11. $$ 49^{-\frac{1}{2}}\left(125^{\frac{2}{3}}-9^{0}\right) = $$ (Calculation not completed)

1 Evaluate without using a calculator:

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Step 1: Evaluate each expression

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