simplify the expression below,using the laws of exponents.
(5^4 x 5^7)/ 5^8
Show your work. PLEASE HELP ME!
x ^ a * x ^ b = x ^ ( a + b )
5 ^ 4 * 5 ^ 7 = 5 ^ ( 4 + 7 ) = 5 ^ 11
x ^ a / x ^ b = x ^ ( a - b )
5 ^ 11 / 5 ^ 8 = 5 ^ ( 11 - 8 ) = 5 ^ 3
5 ^ 4 * 5 ^ 7 / 5 ^ 8 = 5 ^ 3 = 125
x5.x8
To simplify the expression "(5^4 x 5^7) / 5^8" using the laws of exponents, we can apply the rule that states "when dividing two numbers with the same base, subtract the exponents".
Let's break down the expression step by step:
1. Start by multiplying the terms within the parentheses:
5^4 x 5^7 = 5^(4+7) (according to the rule of multiplying exponents with the same base, add the exponents)
= 5^11
2. Now, rewrite the expression:
(5^11) / 5^8
3. Apply the rule for dividing exponents with the same base, which states to subtract the exponents:
5^11 / 5^8 = 5^(11-8)
= 5^3
Therefore, after simplifying the expression using the laws of exponents, we have "5^3" as the final result.
To simplify the given expression (5^4 x 5^7) / 5^8, we can use the properties or laws of exponents.
The property we will use is the product of powers property, which states that when you have the same base number raised to different exponents and are multiplied, you can add the exponents. It can be written as:
a^m x a^n = a^(m+n)
Now let's simplify the expression step by step:
Step 1: Apply the product of powers property.
(5^4 x 5^7) / 5^8 = 5^(4+7) / 5^8
Step 2: Simplify the exponents.
5^(4+7) / 5^8 = 5^11 / 5^8
Step 3: Apply another property of exponents, the quotient of powers property, which states that when you have the same base number raised to different exponents and are divided, you can subtract the exponents. It can be written as:
a^m / a^n = a^(m-n)
Using this property:
5^11 / 5^8 = 5^(11-8)
Step 4: Simplify the exponent.
5^(11-8) = 5^3
Therefore, the simplified expression is 5^3.
Note: If you need the numerical value of 5^3, you can calculate it by multiplying 5 by itself three times:
5^3 = 5 x 5 x 5 = 125
So, the simplified expression is 125.