Which of the following expressions is true?
A)4^3 x 4^4 = 4^12
B)5^2 x 5^3 > 5^5
C)3^2 x 3^5 = 3^10
D)5^2 x 5^4 < 5^8
Which of the following expressions is true?
a)2^4 x 2^3 = 2^12
b)3^3 x 3^6 > 3^8
c)4^2 x 4^2 > 4^4
d)5^2 x 5^2 = 5^10
I don't get how to do these either, can someone please help me on how to find out?
Which of the following expressions is true?
A)4^3 x 4^4 = 4^12
B)5^2 x 5^3 > 5^5
C)3^2 x 3^5 = 3^10
D)5^2 x 5^4 < 5^8
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a^b * a^c = a^(b+c)
so
4^3 * 4^4 = 4^7 not 4^12
5^2*5^3 = 5^5 yes
3^2*3^5 = 3^7 not 3^10
5^6 not 5^8
To determine which expressions are true, we need to understand the properties of exponents. Here's a step-by-step explanation on how to solve these problems:
1. Simplifying Exponents:
- When multiplying two terms with the same base, you can add the exponents. For example, x^a * x^b = x^(a+b).
- When raising a power to another power, multiply the exponents. For example, (x^a)^b = x^(a*b).
2. Evaluating the Expressions:
- Let's apply these rules to the given expressions.
For the first set of expressions:
A) 4^3 x 4^4 = 4^(3+4) = 4^7 = 16384
B) 5^2 x 5^3 = 5^(2+3) = 5^5 = 3125
C) 3^2 x 3^5 = 3^(2+5) = 3^7 = 2187
D) 5^2 x 5^4 = 5^(2+4) = 5^6 = 15625
For the second set of expressions:
a) 2^4 x 2^3 = 2^(4+3) = 2^7 = 128
b) 3^3 x 3^6 = 3^(3+6) = 3^9 = 19683
c) 4^2 x 4^2 = 4^(2+2) = 4^4 = 256
d) 5^2 x 5^2 = 5^(2+2) = 5^4 = 625
3. Comparing the Expressions:
- Now you can compare the simplified expressions to determine which ones are true.
For the first set of expressions:
A) 4^3 x 4^4 = 16384. This is not equal to 4^12, so it is false.
B) 5^2 x 5^3 = 3125. This is less than 5^5, so it is true.
C) 3^2 x 3^5 = 2187. This is not equal to 3^10, so it is false.
D) 5^2 x 5^4 = 15625. This is less than 5^8, so it is true.
For the second set of expressions:
a) 2^4 x 2^3 = 128. This is not equal to 2^12, so it is false.
b) 3^3 x 3^6 = 19683. This is greater than 3^8, so it is true.
c) 4^2 x 4^2 = 256. This is not greater than 4^4, so it is false.
d) 5^2 x 5^2 = 625. This is not equal to 5^10, so it is false.
Based on the above analysis, the true expressions are:
First set: B and D.
Second set: b.
I hope this explanation helps you understand how to solve similar problems in the future!