Math

QuestionSimplify the expression: 5(b3)45(b^{-3})^{4} and expand it to include only positive exponents.

Studdy Solution

STEP 1

Assumptions1. We are given the expression 5(b3)45\left(b^{-3}\right)^{4}. . We need to simplify this expression using the properties of exponents.
3. We should only include positive exponents in our final answer.

STEP 2

To simplify the expression, we first apply the power of a power rule, which states that (am)n=amn(a^m)^n = a^{m \cdot n}.5(b)4=5b45\left(b^{-}\right)^{4} =5b^{- \cdot4}

STEP 3

Calculate the exponent.
5b3=5b125b^{-3 \cdot} =5b^{-12}

STEP 4

Next, we use the rule that an=1ana^{-n} = \frac{1}{a^n} to change the negative exponent to a positive exponent.
b12=1b12b^{-12} = \cdot \frac{1}{b^{12}}

STEP 5

Finally, we simplify the expression by multiplying5 with the fraction.
51b12=5b125 \cdot \frac{1}{b^{12}} = \frac{5}{b^{12}}The simplified expression is 5b12\frac{5}{b^{12}}.

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