Basic Math Examples

${(2 c^{2} d^{0})}^{3 (5 c^{7} + d^{2})}$

Step 1

Simplify the expression.

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Step 1.1

Anything raised to $0$ is $1$ .

${(2 c^{2} \cdot 1)}^{3 (5 c^{7} + d^{2})}$

Step 1.2

Multiply $2$ by $1$ .

${(2 c^{2})}^{3 (5 c^{7} + d^{2})}$

Step 2

Apply the distributive property.

${(2 c^{2})}^{3 (5 c^{7}) + 3 d^{2}}$

Step 3

Simplify the expression.

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Step 3.1

Multiply $5$ by $3$ .

${(2 c^{2})}^{15 c^{7} + 3 d^{2}}$

Step 3.2

Apply the product rule to $2 c^{2}$ .

$2^{15 c^{7} + 3 d^{2}} {(c^{2})}^{15 c^{7} + 3 d^{2}}$

Step 3.3

Multiply the exponents in ${(c^{2})}^{15 c^{7} + 3 d^{2}}$ .

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Step 3.3.1

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

$2^{15 c^{7} + 3 d^{2}} c^{2 (15 c^{7} + 3 d^{2})}$

Step 3.3.2

Apply the distributive property.

$2^{15 c^{7} + 3 d^{2}} c^{2 (15 c^{7}) + 2 (3 d^{2})}$

Step 3.3.3

Multiply $15$ by $2$ .

$2^{15 c^{7} + 3 d^{2}} c^{30 c^{7} + 2 (3 d^{2})}$

Step 3.3.4

Multiply $3$ by $2$ .

$2^{15 c^{7} + 3 d^{2}} c^{30 c^{7} + 6 d^{2}}$