Algebra Examples

${({(4 r^{2} t)}^{3})}^{2}$

Step 1

Multiply the exponents in ${({(4 r^{2} t)}^{3})}^{2}$ .

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Step 1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(4 r^{2} t)}^{3 \cdot 2}$

Step 1.2

Multiply $3$ by $2$ .

${(4 r^{2} t)}^{6}$

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.1

Apply the product rule to $4 r^{2} t$ .

${(4 r^{2})}^{6} t^{6}$

Step 2.2

Apply the product rule to $4 r^{2}$ .

$4^{6} {(r^{2})}^{6} t^{6}$

Step 3

Raise $4$ to the power of $6$ .

$4096 {(r^{2})}^{6} t^{6}$

Step 4

Multiply the exponents in ${(r^{2})}^{6}$ .

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Step 4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$4096 r^{2 \cdot 6} t^{6}$

Step 4.2

Multiply $2$ by $6$ .

$4096 r^{12} t^{6}$