Question

Which expressions represent x with an exponent of 56?

A. x with an exponent of 25 times x with an exponent of 31

B. x with an exponent of 8 times x with an exponent of 7

C. x with an exponent of -73 times x with an exponent of 17

D. (x with an exponent of 4) with an exponent of 14

Answer 1

To determine which expressions represent \(x\) with an exponent of 56, we will simplify each option.

A. \(x^{25} \times x^{31}\)

Using the rule of exponents, \(x^a \times x^b = x^{a+b}\):
\[
x^{25} \times x^{31} = x^{25 + 31} = x^{56}
\]

B. \(x^{8} \times x^{7}\)

Using the same rule:
\[
x^{8} \times x^{7} = x^{8 + 7} = x^{15}
\]

C. \(x^{-73} \times x^{17}\)

Using the exponent rule:
\[
x^{-73} \times x^{17} = x^{-73 + 17} = x^{-56}
\]

D. \((x^4)^{14}\)

Using the power of a power rule, \((x^a)^b = x^{a \cdot b}\):
\[
(x^4)^{14} = x^{4 \times 14} = x^{56}
\]

From the evaluations above:
- A results in \(x^{56}\)
- B results in \(x^{15}\)
- C results in \(x^{-56}\)
- D results in \(x^{56}\)

Thus, the expressions that represent \(x\) with an exponent of 56 are **A and D**.