Apply the Properties of Integer Exponents to generate equivalent expressions to 37⋅3−9 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
37⋅3−9=
To generate an equivalent expression with only positive exponents, we can use the properties of integer exponents.
First, we can rewrite 3^-9 as 1/3^9 since a negative exponent is equivalent to the reciprocal of the base raised to the positive exponent.
So, 37⋅3^-9 is equivalent to 37 * (1/3^9).
To simplify this expression further, we can use the property (a/b)^n = a^n / b^n.
Therefore, 37 * (1/3^9) = 37/3^9.
So, the simplified fraction expression is 37/19683.
Apply the Properties of Integer Exponents to generate equivalent expressions to 3^7⋅3−9 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
3^7⋅3−9=
To generate an equivalent expression with only positive exponents, we can use the properties of integer exponents.
First, we can simplify 3^7⋅3^-9 by subtracting the exponents of the same base, which will result in a positive exponent.
3^7⋅3^-9 = 3^(7+(-9)).
Since 7 + (-9) = -2, we can rewrite the expression as:
3^-2.
To convert this expression into positive exponents, we can use the fact that a negative exponent indicates the reciprocal of the base raised to the positive exponent.
So, 3^-2 is equivalent to 1/3^2.
Simplifying further, 1/3^2 = 1/9.
Therefore, 3^7⋅3^-9 is equal to 1/9.
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 properties of integer exponents.
First, we can simplify 2^2/2^-4 by subtracting the exponents of the same base, which will result in a positive exponent.
2^2/2^-4 = 2^(2-(-4)).
Since 2 - (-4) = 2 + 4 = 6, we can rewrite the expression as:
2^6.
Therefore, 2^2/2^-4 is equal to 2^6.
Simplifying further, 2^6 = 64.
Therefore, 2^2/2^-4 = 64.
Apply the Properties of Integer Exponents to generate equivalent expressions to 40 ⋅ 5−2(−2)−3 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
40 ⋅ 5−2(−2)−3=
To generate an equivalent expression with only positive exponents, we can use the properties of integer exponents.
First, let's focus on the expression within the parentheses: (-2)(-2). According to the property of multiplying exponents with the same base, this can be simplfied as (-2)(-2) = 4.
Now, we can rewrite the expression as:
40 ⋅ 5^-2 ⋅ 4^-3
To simplify further, we can use the property of a negative exponent indicating the reciprocal of the base raised to the positive exponent:
40 ⋅ 1/5^2 ⋅ 1/4^3
Simplifying the exponents further:
40 ⋅ 1/25 ⋅ 1/64
Now, we can multiply these fractions together:
40/25 ⋅ 1/64
Simplifying this further, we can reduce the fraction:
8/5 ⋅ 1/64
Multiplying these fractions together, we get:
8/320
Finally, simplifying this fraction, we get:
1/40
Therefore, 40 ⋅ 5^-2(−2)^-3 is equal to 1/40.