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Chapter 4: Problem 15

Write each expression without using parentheses or negative exponents. Assume no variable is zero. $$\left(b^{4}\right)^{3}\left(b^{2}\right)^{3}$$

Short Answer

Expert verified
The expression \((b^{4})^{3}(b^{2})^{3}\) simplifies to \( b^{18} \).

Step by step solution

01

Simplify \( (b^{4})^{3} \)

Applying the law of exponents that states when you raise a power to a power you multiply the exponents, we get \( b^{4*3} \), which simplifies to \( b^{12} \).
02

Simplify \( (b^{2})^{3} \)

Same as in step 1, we apply the law of exponentiation to get \( b^{2*3} \), which simplifies to \( b^{6} \).
03

Multiply \( b^{12} \times b^{6} \)

Applying the law of exponents that states you add the exponents when multiplying powers with the same base, we get \( b^{12+6} \), which simplifies to \( b^{18} \).

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