Mathematical Comparison: Determining the Greater Value Between Two Numbers

Question

Which value is greater?

00:00 Select the largest value

00:03 When multiplying powers with equal bases

00:06 The power of the result equals the sum of the powers

00:09 When there's a power of a power, the combined power is the product of the powers

00:13 When dividing powers with equal bases

00:16 The power of the result equals the difference of the powers

00:19 We'll determine the largest power, this is the largest value

00:22 This is the solution

To determine which expression has the greatest value, we apply the exponent rules to simplify each choice:

For $x^3 \times x^4$ , using the product rule: $x^3 \times x^4 = x^{3+4} = x^7$ .
For $(x^3)^5$ , using the power of a power rule: $(x^3)^5 = x^{3 \times 5} = x^{15}$ .
$x^{10}$ is already in its simplest form.
For $\frac{x^9}{x^2}$ , using the quotient rule: $\frac{x^9}{x^2} = x^{9-2} = x^7$ .

To identify the greater value, we compare the exponents:

The expression with the largest exponent is $(x^3)^5$ or $x^{15}$ .

Therefore, the expression with the greatest value is $(x^3)^5$ .

$(x^3)^5$