Apply the Properties of Integer Exponents to generate equivalent expressions to 222−4 with only positive exponents, then solve the expression. Provide the solution as a whole number.(1 point)
222−4=
Which of the following is an equivalent expression to 59⋅5−13 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses
154
Start Fraction 1 over 5 superscript 4 baseline end fraction
595−13
Start Fraction 5 superscript 9 baseline over 5 superscript negative 13 baseline End Fraction
1625
Start Fraction 1 over 625 end fraction
54
To generate an equivalent expression with only positive exponents, we can use the property that a negative exponent on a number can be written as the reciprocal of the number with a positive exponent.
So, 59⋅5^-13 can be rewritten as 59/(5^13).
Therefore, the equivalent expression with only positive exponents is 59/(5^13), which is not one of the provided options.
Which of the following is an equivalent expression to 150 ⋅ 7−2 (−4)−3 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses
4372
Start Fraction 4 cubed over 7 squared end fraction
72(−4)3
Start Fraction 7 squared over left parenthesis negative 4 right parenthesis cubed end fraction
(−4)372
start fraction left parenthesis negative 4 right parenthesis cubed over 7 squared end fraction
172 ⋅ (−4)−3
To generate an equivalent expression with only positive exponents, we can use the property that a negative exponent on a number can be written as the reciprocal of the number with a positive exponent.
So, 150 ⋅ 7^-2 (-4)^-3 can be rewritten as 150/(7^2 * (-4)^3).
Therefore, the equivalent expression with only positive exponents is 150/(7^2 * (-4)^3), which is not one of the provided options.
Apply the Properties of Integer Exponents to generate equivalent expressions to 2^2/2^−4 with only positive exponents, then solve the expression. Provide the solution as a whole number.(1 point)
2^2/2^−4=
To generate an equivalent expression with only positive exponents, we can use the property of integer exponents which states that a negative exponent can be rewritten as the reciprocal of the base with a positive exponent.
In this case, we have 22^(-4). We can rewrite this expression by using the property mentioned above:
22^(-4) = 1 / 22^4
Now, we can solve this expression by evaluating 22^4.
To do this, we need to understand that 22^4 means multiplying 22 by itself four times:
22^4 = 22 * 22 * 22 * 22
Calculating this expression, we get:
22^4 = 14,641
Now, substitute this value back into the original expression:
1 / 22^4 = 1 / 14,641
Simplifying this expression, we find that 222^(-4) is equivalent to 1 / 14,641.
As the question asks for the solution as a whole number, the simplified expression 1 / 14,641 cannot be further simplified. Therefore, the solution is 1 / 14,641.
To apply the properties of integer exponents and generate an equivalent expression with only positive exponents, we can use the property that a negative exponent on a number can be written as the reciprocal of the number with a positive exponent.
So, 222^-4 can be rewritten as 1/(222^4).
To solve this expression, we can evaluate 222^4.
222^4 = 222 * 222 * 222 * 222 = 2342568000
Therefore, 222^-4 = 1/2342568000.
The solution as a whole number is 1/2342568000.