This math topic involves solving problems related to the difference and sum of exponential terms of variables, then dividing by the smaller exponent and solving for the variable without a calculator. Each problem presents an equation with the variable in an exponential form set equal to a numerical value, challenging skills in polynomial algebra and exponent manipulation. This topic is advanced, focusing on solving polynomial and quadratic equations, especially dealing with exponents in algebraic expressions.

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Polynomial Algebra - Difference of Exponents (Variables) Divided by Second Exponent - Solve Worksheet

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Polynomial Algebra - Difference of Exponents (Variables) Divided by Second Exponent - Solve
1
Find the value of x without using a calculator
A LaTex expression showing \frac{x to the power of 279 - x to the power of 278 }{x to the power of 278 } = 16
a
x = 18
b
x = 25
c
x = 20
d
x = 14
e
x = 17
f
x = 23
2
Find the value of n without using a calculator
A LaTex expression showing \frac{n to the power of 486 - n to the power of 485 }{n to the power of 485 } = 6
a
n = 13
b
n = 6
c
n = 8
d
n = 5
e
n = 3
f
n = 7
3
Find the value of x without using a calculator
A LaTex expression showing \frac{x to the power of 298 + x to the power of 297 }{x to the power of 297 } = 16
a
x = 16
b
x = 17
c
x = 9
d
x = 14
e
x = 15
f
x = 10
4
Find the value of y without using a calculator
A LaTex expression showing \frac{y to the power of 451 + y to the power of 450 }{y to the power of 450 } = 9
a
y = 2
b
y = 17
c
y = 11
d
y = 6
e
y = 16
f
y = 8
5
Find the value of m without using a calculator
A LaTex expression showing \frac{m to the power of 306 - m to the power of 305 }{m to the power of 305 } = 11
a
m = 2
b
m = 12
c
m = 11
d
m = 18
e
m = 4
f
m = 7
6
Find the value of m without using a calculator
A LaTex expression showing \frac{m to the power of 146 + m to the power of 145 }{m to the power of 145 } = 10
a
m = 6
b
m = 14
c
m = 12
d
m = 9
e
m = 3
f
m = 1
7
Find the value of d without using a calculator
A LaTex expression showing \frac{d to the power of 210 + d to the power of 209 }{d to the power of 209 } = 7
a
d = 8
b
d = 6
c
d = 4
d
d = 10
e
d = 15
f
d = 9
8
Find the value of m without using a calculator
A LaTex expression showing \frac{m to the power of 347 - m to the power of 346 }{m to the power of 346 } = 22
a
m = 33
b
m = 23
c
m = 17
d
m = 35
e
m = 19
f
m = 29