524. Förenkla och skriv ut talet. $$ \begin{array}{ll} ext { a) }\left(10^{2} ight)^{3} \cdot 10^{4} & ext { b) } 10^{3} \cdot 10^{-5} \cdot 10^{8} \ ext { c) } 10^{-3} \cdot\left(10^{3} ight)^{2} & ext { d) } 10^{4} \cdot\left(10^{-2} ight)^{3}\end{array} $$

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524. Förenkla och skriv ut talet. $$ \begin{array}{ll}	ext { a) }\left(10^{2}ight)^{3} \cdot 10^{4} & 	ext { b) } 10^{3} \cdot 10^{-5} \cdot 10^{8} \ 	ext { c) } 10^{-3} \cdot\left(10^{3}ight)^{2} & 	ext { d) } 10^{4} \cdot\left(10^{-2}ight)^{3}\end{array} $$

UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$10^{-3}\left(10^{3}\right)^{2}$$
- step1: Multiply the exponents:
  $$10^{-3}\times 10^{3\times 2}$$
- step2: Multiply the numbers:
  $$10^{-3}\times 10^{6}$$
- step3: Multiply:
  $$10^{-3+6}$$
- step4: Add the numbers:
  $$10^{3}$$
- step5: Evaluate the power:
  $$1000$$
Calculate or simplify the expression $$ (10^2)^3 * 10^4 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(10^{2}\right)^{3}\times 10^{4}$$
- step1: Multiply the exponents:
  $$10^{2\times 3}\times 10^{4}$$
- step2: Multiply the numbers:
  $$10^{6}\times 10^{4}$$
- step3: Multiply:
  $$10^{6+4}$$
- step4: Add the numbers:
  $$10^{10}$$
Calculate or simplify the expression $$ 10^3 * 10^{-5} * 10^8 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$10^{3}\times 10^{-5}\times 10^{8}$$
- step1: Multiply the terms:
  $$10^{3-5+8}$$
- step2: Calculate:
  $$10^{6}$$
Calculate or simplify the expression $$ 10^4 * (10^{-2})^3 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$10^{4}\left(10^{-2}\right)^{3}$$
- step1: Multiply the exponents:
  $$10^{4}\times 10^{-2\times 3}$$
- step2: Multiply the numbers:
  $$10^{4}\times 10^{-6}$$
- step3: Multiply:
  $$10^{4-6}$$
- step4: Subtract the numbers:
  $$10^{-2}$$
- step5: Express with a positive exponent:
  $$\frac{1}{10^{2}}$$
- step6: Evaluate the power:
  $$\frac{1}{100}$$
Här är förenklingarna av de givna uttrycken:

a) $$ (10^{2})^{3} \cdot 10^{4} $$

Förenkling:
$$
(10^{2})^{3} = 10^{2 \cdot 3} = 10^{6}
$$
Därefter:
$$
10^{6} \cdot 10^{4} = 10^{6 + 4} = 10^{10}
$$

**Resultat:** $$ 10^{10} $$

---

b) $$ 10^{3} \cdot 10^{-5} \cdot 10^{8} $$

Förenkling:
$$
10^{3} \cdot 10^{-5} \cdot 10^{8} = 10^{3 - 5 + 8} = 10^{6}
$$

**Resultat:** $$ 10^{6} $$ eller $$ 1000000 $$

---

c) $$ 10^{-3} \cdot (10^{3})^{2} $$

Förenkling:
$$
(10^{3})^{2} = 10^{3 \cdot 2} = 10^{6}
$$
Därefter:
$$
10^{-3} \cdot 10^{6} = 10^{-3 + 6} = 10^{3}
$$

**Resultat:** $$ 1000 $$

---

d) $$ 10^{4} \cdot (10^{-2})^{3} $$

Förenkling:
$$
(10^{-2})^{3} = 10^{-2 \cdot 3} = 10^{-6}
$$
Därefter:
$$
10^{4} \cdot 10^{-6} = 10^{4 - 6} = 10^{-2}
$$

**Resultat:** $$ 10^{-2} $$ eller $$ 0.01 $$

---

Sammanfattning av resultaten:
- a) $$ 10^{10} $$
- b) $$ 10^{6} $$ eller $$ 1000000 $$
- c) $$ 1000 $$
- d) $$ 10^{-2} $$ eller $$ 0.01 $$
a) $$ 10^{10} $$ b) $$ 10^{6} $$ eller $$ 1000000 $$ c) $$ 1000 $$ d) $$ 10^{-2} $$ eller $$ 0.01 $$

Förenkla och skriv ut talet.

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