Simplify each expression and eliminate any negative exponents.
(a)
(b)
©

Ask by Wright Carrillo. in the United States

Jan 24,2025

Question

Simplify each expression and eliminate any negative exponents. (a) $$ a^{7} a^{8} $$ (b) $$ \left(-2 b^{-7}\right)^{3} $$ (c) $$ -2 y^{16} y^{-17} $$

UpStudy AI · Accepted Answer

Let's simplify each expression step-by-step and eliminate any negative exponents.

### (a) $$ a^{7} a^{8} $$

When multiplying expressions with the same base, add the exponents:
$$
a^{7} \cdot a^{8} = a^{7+8} = a^{15}
$$
**Simplified Expression:** $$ a^{15} $$

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### (b) $$ \left(-2 b^{-7}\right)^{3} $$

First, apply the exponent to both the coefficient and the variable:
$$
\left(-2 b^{-7}\right)^{3} = (-2)^{3} \cdot \left(b^{-7}\right)^{3} = -8 \cdot b^{-21}
$$
To eliminate the negative exponent, rewrite $$ b^{-21} $$ as $$ \frac{1}{b^{21}} $$:
$$
-8 \cdot b^{-21} = \frac{-8}{b^{21}}
$$
**Simplified Expression:** $$ \frac{-8}{b^{21}} $$

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### (c) $$ -2 y^{16} y^{-17} $$

Combine the exponents using the rule $$ y^{a} \cdot y^{b} = y^{a+b} $$:
$$
y^{16} \cdot y^{-17} = y^{16-17} = y^{-1}
$$
Now, rewrite $$ y^{-1} $$ to eliminate the negative exponent:
$$
-2 y^{-1} = \frac{-2}{y}
$$
**Simplified Expression:** $$ \frac{-2}{y} $$

---

### Final Answers:

a) $$ a^{15} $$

b) $$ \dfrac{-8}{b^{21}} $$

c) $$ \dfrac{-2}{y} $$
a) $$ a^{15} $$ b) $$ \frac{-8}{b^{21}} $$ c) $$ \frac{-2}{y} $$

Simplify each expression and eliminate any negative exponents.
(a)
(b)
©

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Simplify each expression and eliminate any negative exponents. (a) (b) ©