Which of the following is an equivalent expression to 5^9x5^-13with only positive exponents that has been generated by applying the Properties of Integer Exponents? (1 point)
The answer is 1/5^4
Btw ^ means when the number is like the power of, like they small number lol.
5^-4
ARE YOU SURE
Apologies for the error in my previous response. Let's try again.
An equivalent expression to 5^9x5^-13 with only positive exponents can be generated by applying the property of exponents that states a^m/a^n = a^(m-n) when a ≠ 0:
= 5^(9-13)
= 5^(-4)
So, the equivalent expression is 5^(-4)
Which of the following is an equivalent expression to 15^0x7^-2/(-4)^-3 with only positive exponents that has been generated by applying the Properties of Integer Exponents? ( point)
To simplify the expression and generate an equivalent expression with only positive exponents, we can use the properties of exponentiation.
We know that any number, except for 0, raised to the power of 0 is equal to 1. Therefore, 15^0 = 1.
Next, we can apply the property of a negative exponent, which states that a negative exponent can be rewritten as 1 divided by the base raised to the positive exponent. That is, a^(-n) = 1/a^n.
So, 7^-2 = 1/7^2 = 1/49.
Similarly, (-4)^-3 = 1/(-4)^3 = 1/(-64) = -1/64.
Now, we can substitute these values back into the expression:
15^0 x 7^-2 / (-4)^-3
= 1 x 1/49 / -1/64
= 1/49 / -1/64
= (1/49) x (-64/1)
= -64/49
Therefore, the equivalent expression with only positive exponents is -64/49.
Wrong, it’s looking for and equivalent answer, not the solved answer.
Apologies for the confusion. Let's generate an equivalent expression with only positive exponents without simplifying further.
Given expression: 15^0x7^-2/(-4)^-3
We can use the property of a negative exponent to move the negative exponents to the denominator or numerator, depending on its original placement.
15^0x7^-2/(-4)^-3
= 1 * 1/15^0 * 1/7^2 * (-4)^3
Since any number (except 0) raised to the power of 0 is 1, we can simplify further:
= 1 * 1 * 1/49 * (-4)^3
Now, applying the property of a negative exponent to -4 raised to the power of 3:
= 1 * 1 * 1/49 * (-1/4)^3
This can still be simplified by applying the property of a power of a quotient:
= 1 * 1 * 1/49 * (-1)^3/(4)^3
= 1 * 1 * 1/49 * -1/64
Now, combining the numerical values:
= -1/3136
Therefore, an equivalent expression with only positive exponents is -1/3136.
hey bot
To find an equivalent expression with positive exponents for 5^9 * 5^-13, we can make use of the property of integer exponents: a^m * a^n = a^(m+n).
So, we can rewrite the expression as 5^(9 + (-13)).
To simplify further, we add the exponents: 9 + (-13) = -4.
Therefore, the equivalent expression with positive exponents is 5^-4.