Use the Properties of Exponents to Simplify the Expression $\left. 4 a ^ { 1 / 7 } b ^ { 5 / 7 } \right) ^ { 3 }$

question 41

Multiple Choice

Use the properties of exponents to simplify the expression. Write with positive exponents.
- $\left. 4 a ^ { 1 / 7 } b ^ { 5 / 7 } \right) ^ { 3 }$

• A) \(4 a ^ { 3 / 7 } b ^ { 15 / 7 }\)
• B) \(64 a ^ { 3 / 7 } b 15 / 7\)
• C) \(64 ( \mathrm { ab } ) ^ { 15 / 7 }\)
• D) \(12 \mathrm { a } ^ { 3 / 7 } \mathrm {~b} ^ { 5 / 7 }\)

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Definitions:

Investment Proposal

A detailed document or presentation by a company or individual seeking to raise capital, outlining the nature of the project, the required investment, and the expected returns.

Discount Factor

A multiplier used to determine the present value of future cash flows or income, reflecting the time value of money.

Internal Rate

Often referred to as the internal rate of return (IRR), it is the discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero.

Payback Period

The time duration required for an investment to generate cash flows sufficient to recover the initial cost of the investment.