apply the property of negative integer exponents to generate an expression equivalent to 3^-17/8^-14 with positive exponents only
To apply the property of negative integer exponents, we can reciprocate the fractions and change the sign of the exponents.
The expression 3^-17/8^-14 can be written as (1/3^17)/(1/8^14).
Reciprocating the fractions and changing the sign of the exponents, we get (8^14)/(3^17).
So, the expression with positive exponents only that is equivalent to 3^-17/8^-14 is 8^14/3^17.
apply the property of integer exponents to generate expressions equivalent to (7^-3)^7 x 7^20/6^-2 with positive exponents only then solve the expression. Provide the answer as a improper fraction
To apply the property of integer exponents, we can simplify the expression step by step:
First, let's simplify (7^-3)^7. To simplify a power raised to another power, we multiply the exponents. So (7^-3)^7 becomes 7^(-3*7) = 7^-21.
Next, let's simplify 7^20/6^-2. To simplify a fraction with powers, we subtract the exponents in the denominator from the exponents in the numerator. So 7^20/6^-2 becomes 7^20 * 6^2.
Now, we can combine the two simplified expressions. So our expression becomes: 7^-21 * 7^20 * 6^2.
To simplify this, we add the exponents when multiplying with the same base. So 7^-21 * 7^20 becomes 7^(-21+20) = 7^-1.
Finally, our expression becomes 7^-1 * 6^2 = 1/7^1 * 6^2 = 1/7 * 6^2 = 36/7.
Therefore, the simplified and solution of the expression (7^-3)^7 x 7^20/6^-2 with positive exponents only is 36/7 as an improper fraction.
Simplify the Expression (4x³)² using the properties of integer exponents
8x⁶
4x⁶
16x⁵
16x⁶
To apply the property of negative integer exponents and generate an expression with positive exponents only for 3^(-17)/8^(-14), we can use the rule that says:
"a^(-b) = 1 / (a^b)"
Using this rule, we can rewrite the expression as:
3^(-17) / 8^(-14) = (1 / 3^17) / (1 / 8^14)
Next, we can apply the property of division of exponents, which states:
"a^b / a^c = a^(b - c)"
Applying this rule, we can simplify the expression:
(1 / 3^17) / (1 / 8^14) = 8^14 / 3^17
So the expression with positive exponents only equivalent to 3^(-17) / 8^(-14) is 8^14 / 3^17.
To apply the property of negative integer exponents and rewrite the expression 3^-17/8^-14 with positive exponents only, we need to use the rule:
a^-n = 1/a^n
Let's apply this rule to the given expression:
3^-17/8^-14
The numerator, 3^-17, becomes 1/3^17
The denominator, 8^-14, becomes 1/8^14
Now, let's rewrite the expression with positive exponents only:
(1/3^17) / (1/8^14)
To simplify further, we can multiply the numerator and denominator by the reciprocal of the denominator:
(1/3^17) * (8^14/1)
Now, we can simplify this expression by applying the rule of multiplication for exponents. Multiply the exponents of the same base:
1 * 8^14 / 3^17
This results in a final expression equivalent to 3^-17/8^-14 with positive exponents only:
8^14/3^17