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Simplify the following exponential expressions: 2.1) (a3)4 2.2) 4a1b3 imes -3a3b1

May 9, 2026Mathematics

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2 parts

a^{12}

-12a^4b^4

6 steps

Here are the solutions for 2.1 and 2.2.

Apply the power of a power rule for exponents, which states that $(x^m)^n = x^{m \cdot n}$ .
$(a^3)^4 = a^{3 \times 4}$
Multiply the exponents.
$a^{3 \times 4} = a^{12}$
The simplified expression is:
$\boxed{a^{12}}$

Multiply the numerical coefficients.
$4 \times -3 = -12$
Multiply the terms with the base $a$ .
Remember that $a$ is $a^1$ .
$a^1 \times a^3 = a^{1+3} = a^4$
Multiply the terms with the base $b$ .
Remember that $b$ is $b^1$ .
$b^3 \times b^1 = b^{3+1} = b^4$
Combine the results from Step 1, Step 2, and Step 3.
$-12 \cdot a^4 \cdot b^4 = -12a^4b^4$
The simplified expression is:
$\boxed{-12a^4b^4}$

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