Apply the Properties of Integer Exponents to generate equivalent expressions to 3^7 • 4^-9 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.
If you have time can you put the correct answers in please, The Bot is sometimes incorrect because one time for math I got a 1 out of 5 so, please make sure you or anyone who sees this comment please put the right answers in after you are done with your assignment because we need to know what the right answers are, not what the Bot decides to say.
To generate equivalent expressions with only positive exponents, we use the properties of integer exponents.
First, let's rewrite the expression 4^-9 as (1/4)^9. This is because any non-zero number raised to the power of -n is equivalent to 1 divided by the same number raised to the power of n.
Now, let's simplify the expression using the properties of exponents:
3^7 • 4^-9 = (3^7)(1/4^9)
Since both 3 and 4 are prime numbers, we cannot simplify any further using the properties of exponents.
To solve the expression, we can evaluate the powers of 3 and 4:
(3^7)(1/4^9) = 2187(1/262144)
Now, let's simplify this fraction. The numerator, 2187, and the denominator, 262144, have no common factors other than 1. Therefore, the fraction is already simplified.
Therefore, the simplified fraction is:
2187/262144
3^7 • 4^-9
To generate equivalent expressions with only positive exponents, we can apply the property (a^m) • (a^n) = a^(m + n).
So, let's apply this property to simplify the expression:
3^7 • 4^-9
= 3^7 • (1/4^9)
= 3^7 • 1/(4^9)
= 3^7/4^9
Now, let's further simplify the expression by evaluating the powers of 3 and 4:
= (3 • 3 • 3 • 3 • 3 • 3 • 3) / (4 • 4 • 4 • 4 • 4 • 4 • 4 • 4 • 4)
= 2187 / 262144
Therefore, the simplified fraction is 2187/262144.
Apply the Properties of Integer Exponents to the equation
To apply the properties of integer exponents to the equation 3^7 • 4^-9, we can use the property a^m • a^n = a^(m + n) to combine the exponents:
3^7 • 4^-9 = 3^7 • (1/4^9)
Next, we can use the property (a/b)^-n = b^n/a^n to move the negative exponent from the numerator to the denominator:
= 3^7 • (4^9/1^9)
Simplifying the expression further, we have:
= 3^7 • 4^9
Lastly, we can directly calculate the value of the expression by evaluating the powers:
= (3 • 3 • 3 • 3 • 3 • 3 • 3) • (4 • 4 • 4 • 4 • 4 • 4 • 4 • 4 • 4)
= 2187 • 262144
Therefore, the simplified value of the expression is 574,962,048.