Math  /  Algebra

Question(a7)5\left(a^{7}\right)^{5}

Studdy Solution

STEP 1

What is this asking? We're asked to simplify an expression with an exponent raised to another exponent, which means we'll need to use our exponent rules! Watch out! Don't accidentally multiply the base by the exponent.
Remember, exponents represent repeated multiplication.

STEP 2

1. Apply the power of a power rule.

STEP 3

When you have a power raised to another power, like (am)n(a^m)^n, you **multiply** the exponents.
This means (am)n=amn(a^m)^n = a^{m \cdot n}.
It's like having *m* groups of *n* *a*'s multiplied together, which is a total of mnm \cdot n *a*'s multiplied together.

STEP 4

In our case, we have (a7)5(a^7)^5.
Our 'inside' exponent is m=7m = \mathbf{7} and our 'outside' exponent is n=5n = \mathbf{5}.
So, we **multiply** those exponents: 75=357 \cdot 5 = \mathbf{35}.

STEP 5

Therefore, (a7)5=a75=a35(a^7)^5 = a^{7 \cdot 5} = a^{\mathbf{35}}.

STEP 6

Our simplified expression is a35a^{35}.

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