Which of the following is the equivalent expression to (15−3 ⋅ 47)04−3 that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses
164
Start Fraction 1 over 64 end fraction
1⋅4−3
1 times 4 negative cubed
604−3
Start Fraction 60 over 4 negative cubed end fraction
64
Start Fraction 1 over 64 end fraction
To find the equivalent expression generated by applying the properties of integer exponents, let's simplify (15 - 3 ⋅ 47)04 - 3 step-by-step.
Step 1: Evaluate the exponent first
The expression becomes (15 - 3 ⋅ 47)01 - 3
Step 2: Apply the product rule of exponents
The expression becomes (15 - 141)01 - 3
Step 3: Simplify the subtraction
The expression becomes (-126)01 - 3
Step 4: Apply the zero exponent property
The expression becomes 1 - 3
Step 5: Simplify the exponent
The expression becomes 1⋅4-3
Step 6: Apply the power rule of exponents
The expression simplifies to 64.
Therefore, the equivalent expression, generated by applying the properties of integer exponents, is 64.