Question

Difficulty: EasyOperations with Variable Exponents

If the equation $y^8 \cdot y^k = y^{15}$ is true for all non-zero values of $y$ , what is the value of $k$ ?

Answer: 7 / seven

The correct value of

k

7

because applying the product rule of exponents gives

y^8 \cdot y^7 = y^{8+7} = y^{15}

Apply the product rule for exponents to the left side of the equation.

y^8 \cdot y^k = y^{8+k}

When multiplying exponential expressions with the same base, the exponents are added.

Set the exponent of the simplified left side equal to the exponent of the right side.

8 + k = 15

Since the bases are equal and non-zero, their exponents must be equal.

Solve the linear equation for

k

k = 7

Subtracting 8 from both sides of the equation isolates the variable

k

Product Rule for Exponents

Rate this question

Topics