Start Fraction 144 superscript 14 baseline over 144 squared End Fraction
A. 14416
B. 14412
C. 14428
D. 144 superscript fourteen-halves baseline
The correct answer is D.
To solve this, first simplify the fraction by dividing both the numerator and the denominator by 144.
This gives us:
(144^14 / 144^2) = 144^(14-2) = 144^12
Therefore, the answer is 144 superscript twelve baseline.
Start Fraction x superscript 16 baseline over x superscript 3 baseline End Fraction
A. Lower x superscript Start Fraction 16 over 3 End Fraction baseline
B. x48
C. x19
D. x13
The correct answer is A. Lower x superscript Start Fraction 16 over 3 End Fraction baseline.
To simplify the given expression, we can apply the rule of exponents that states when we divide two exponential expressions with the same base, we subtract their exponents. So,
(x^16) / (x^3) = x^(16-3) = x^13
Now, we need to convert this result into the required format, which is in terms of an exponent that is a fraction with the denominator of 3.
We can rewrite x^13 as x^(13/1), which means the denominator is 1 and we need to express the exponent with a denominator of 3.
To do this, we can multiply both the numerator and denominator of the exponent by 3:
x^(13/1) * (3/3) = x^(39/3)
Simplifying the exponent gives us:
x^(39/3) = x^(13)
Therefore, the answer is A. Lower x superscript Start Fraction 16 over 3 End Fraction baseline.
Which of the following expressions is true?
A. 43 • 44 = 412
B. 52 • 53 > 55
C. 32 • 35 < 38
D. 52 • 54 = 58
The correct answer is C. 32 • 35 < 38.
To determine if an expression is true, we need to evaluate each side of the inequality and compare the results.
A. 43 • 44 = 1892
This is not true, as 43 • 44 equals 1892, not 412.
B. 52 • 53 > 55
This is not true, as 52 • 53 equals 2756, which is greater than 55.
C. 32 • 35 < 38
This is true, as 32 • 35 equals 1120, which is less than 38.
D. 52 • 54 = 58
This is not true, as 52 • 54 equals 2808, not 58.
Therefore, the only expression that is true is C. 32 • 35 < 38.
Start Fraction x superscript 13 baseline over x squared End Fraction
To simplify the given expression:
Start Fraction x superscript 13 baseline over x squared End Fraction
We can use the rule of exponents that states when we divide two exponential expressions with the same base, we subtract their exponents. In this case, since the base is x, we can write:
Start Fraction x superscript 13 baseline over x squared End Fraction = x^(13-2) = x^11
Therefore, the simplified expression is x^11.
Which of the following expressions is true?
A. 43 • 44 = 412
B. 52 • 53 > 55
C. 32 • 35 < 38
D. 52 • 54 = 58
The correct answer is C. 32 • 35 < 38.
To solve this question, we need to evaluate each expression and compare the results.
A. 43 • 44 = 1892
This is not true, as 43 • 44 equals 1892.
B. 52 • 53 > 55
This is not true, as 52 • 53 equals 2756, which is greater than 55.
C. 32 • 35 < 38
This is true, as 32 • 35 equals 1120, which is less than 38.
D. 52 • 54 = 58
This is not true, as 52 • 54 equals 2808.
Therefore, the only true expression is C. 32 • 35 < 38.
Which of the following expressions is true?
A. 4^3 • 4^4 = 4^12
B. 5^2 • 5^3 > 5^5
C. 3^2 • 3^5 < 3^8
D. 5^2 • 5^4 = 5^8