How do you simplify #4^ { 9} \div \frac { 4^ { 5} } { 4^ { - 8} } #?

Answer 1

Isaiah Anthony

Set up the problem as a complex fraction and divide out exponents

As a complex fraction the problem can be rewritten as

#( 4^9/1)/( 4^5/4^-8)#

To simply a complex fraction multiply both the top and the bottom fractions by the inverse io the bottom fraction

# {4^9/1 xx 4^-8/4^5}/{4^5/4^-8 xx 4^-8/4^5}#

The bottom fractions turn into 1 and disappear. leaving

# 4^9/1 xx 4^-8/4^5# Multiplying exponents is the same as adding them so

#( 4^+(9-8))/4^5# This gives

# 4^1/4^5 # = # 1/4^4 # =# 4^-4#

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email

Answer 2

Isaiah Anthony

To simplify $4^9 \div \frac{4^5}{4^{-8}}$ , you can use the properties of exponents. First, simplify the expression inside the division:

$4^9 \div \frac{4^5}{4^{-8}} = 4^9 \div 4^5 \cdot 4^8$

Next, use the property of division of exponents, which states that $a^m \div a^n = a^{m-n}$ :

$4^9 \div 4^5 \cdot 4^8 = 4^{9-5} \cdot 4^8 = 4^4 \cdot 4^8$

Now, use the property of multiplication of exponents, which states that $a^m \cdot a^n = a^{m+n}$ :

$4^4 \cdot 4^8 = 4^{4+8} = 4^{12}$

Therefore, $4^9 \div \frac{4^5}{4^{-8}}$ simplifies to $4^{12}$ .

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.