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
1⋅4−3
1 times 4 negative cubed
604−3
Start Fraction 60 over 4 negative cubed end fraction
164
Start Fraction 1 over 64 end fraction
64
Start Fraction 1 over 64 end fraction
To find the equivalent expression of (15−3 ⋅ 47)04−3 using properties of integer exponents, we can simplify the calculations step by step:
1. Simplify the exponent 15−3 to (1/125)
2. Simplify the exponent 04−3 to (1/64)
3. Multiply the simplified exponents: (1/125) times (1/64)
Therefore, the equivalent expression is 1/8,192, which can be written as 1/64.
To find the equivalent expression to (15 - 3 * 47)04 - 3 using the Properties of Integer Exponents, we need to understand the rules involved.
The first rule is the Product of Powers Property, which states that when you multiply two numbers with the same base but different exponents, you can add the exponents together.
The second rule is the Power of a Power Property, which states that when you raise a power to another power, you multiply the exponents together.
Now let's simplify the expression step by step:
1. Start with (15 - 3 * 47)04 - 3.
2. Simplify the multiplication within the parentheses: (15 - 141)04 - 3.
3. Simplify further within the parentheses: (-126)04 - 3.
4. Apply the Power of a Power Property to the exponent outside the parentheses: -12604 - 3.
5. Now, apply the Product of Powers Property by multiplying -126 to 4: -504 - 3.
6. Finally, simplify the expression: -507.
So, the equivalent expression using the Properties of Integer Exponents is -507.
Therefore, the correct response is 164, as none of the options matches the rules and steps explained above.