Apply the property of negative integer exponents to solve 3^-4. The answer should not contain any exponent expression or decimals.
To solve 3^-4 using the property of negative integer exponents, we can rewrite it as the reciprocal of 3^4.
3^-4 = 1/(3^4)
Now, let's evaluate 3^4:
3^4 = 3 * 3 * 3 * 3 = 81
So, 3^-4 = 1/81.
Thus, the answer is 1/81.
Apply the property of negative integer exponents to generate an expression equivalent to 7^-³ • 7^-⁵ with positive exponents only.
To generate an expression equivalent to 7^-³ • 7^-⁵ with positive exponents only, we can apply the property of negative exponents which states that any number raised to a negative exponent is equal to its reciprocal raised to the positive exponent.
Let's rewrite 7^-³ as 1/7³ and 7^-⁵ as 1/7⁵:
1/7³ • 1/7⁵
Now, we can combine these two fractions by multiplying the numerators and the denominators:
(1 • 1) / (7³ • 7⁵)
Simplifying:
1 / 7^(3 + 5)
1 / 7^8
So, the expression equivalent to 7^-³ • 7^-⁵ with positive exponents only is 1/7^8.
Apply the property of negative integer exponents to generate an expression equivalent to 5^-⁹/4^-¹²
With positive exponents only.
To generate an expression equivalent to 5^-⁹/4^-¹² with positive exponents only, we can use the property of negative exponents, which states that any number raised to a negative exponent is equal to its reciprocal raised to the positive exponent.
First, we rewrite 5^-⁹ as 1/5^⁹ and 4^-¹² as 1/4^-¹².
Now, let's substitute these values into the expression:
(1/5^⁹)/(1/4^-¹²)
Using the property of dividing fractions (invert and multiply):
(1/5^⁹) * (4^-¹²/1)
To simplify this expression, we can multiply the numerators and denominators separately:
1 * 4^-¹² / 5^⁹
Since 4^-¹² is the reciprocal of 4¹², we can write it as 1/4¹²:
(1/4¹²) / 5^⁹
Now, we can rewrite 5^⁹ as (1/5^-⁹):
(1/4¹²) / (1/5^-⁹)
Applying the property of dividing by a fraction (multiply by its reciprocal):
(1/4¹²) * (5^-⁹/1)
Multiplying the numerators and denominators separately:
1 * 5^-⁹ / 4¹² * 1
Therefore, the expression equivalent to 5^-⁹/4^-¹² with positive exponents only is 5^-⁹ / 4¹².
Wrong
To generate an expression equivalent to 5^-⁹/4^-¹² with positive exponents only, we can apply the property of negative exponents, which states that any number raised to a negative exponent is equal to its reciprocal raised to the positive exponent.
First, let's rewrite 5^-⁹ as 1/5^⁹ and 4^-¹² as 1/4^¹².
Now, we can substitute these values into the expression:
1/(5^⁹) / 1/(4^¹²)
To divide fractions, we invert the second fraction and multiply:
1/(5^⁹) * (4^¹²/1)
Multiplying the numerators and denominators separately:
(1 * 4^¹²) / (5^⁹ * 1)
Simplifying:
4^¹² / 5^⁹
Thus, the expression equivalent to 5^-⁹/4^-¹² with positive exponents only is 4^¹² / 5^⁹.