Pre-Algebra Examples

$7^{x} \cdot {(7^{5})}^{4} = 7^{14}$

Step 1

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

$7^{x} \cdot 7^{5 \cdot 4} = 7^{14}$

Step 2

Multiply $7^{x}$ by $7^{5 \cdot 4}$ by adding the exponents.

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Step 2.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$7^{x + 5 \cdot 4} = 7^{14}$

Step 2.2

Multiply $5$ by $4$ .

$7^{x + 20} = 7^{14}$

Step 3

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$x + 20 = 14$

Step 4

Move all terms not containing $x$ to the right side of the equation.

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Step 4.1

Subtract $20$ from both sides of the equation.

$x = 14 - 20$

Step 4.2

Subtract $20$ from $14$ .

$x = - 6$