Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

The problem asks to simplify the expression $\frac{4^{x+1} \times 8^{2x}}{2^{x+3}}$.

ExponentsSimplificationAlgebraic Manipulation

Solve the inequality $-4 > (x-5)(x+5) - (x-3)^2$ for $x$.

InequalitiesQuadratic ExpressionsAlgebraic Manipulation

We are asked to solve the equation $3^{x+2} - 6 \cdot 3^x + 5 \cdot 3^{x-2} = 0$ for $x$.

ExponentsEquationsExponential EquationsNo Solution

We need to solve the equation: $3^{x+2} - 6 \cdot 3^x + 5 \cdot 3^{x-2} = 0$ for $x$.

Exponential EquationsExponent RulesSolving Equations

We are asked to simplify the expression $3^{x+2} - 6 \times 3^x + 5 \times 3^{x-2}$.

ExponentsSimplificationAlgebraic Manipulation

We are asked to simplify the expression $3^{x+2} - 6 \cdot 3^x + 5 \cdot 3^{x-2}$.

ExponentsSimplificationAlgebraic Manipulation

The problem states that we have an increasing arithmetic sequence ${a_n}$. The first term $a_1 = 2$....

Arithmetic SequenceGeometric SequenceSequences and SeriesCommon Difference

We are given an arithmetic sequence $\{a_n\}$ with the first term $a_1 = 2$ and common difference $d...

SequencesSeriesArithmetic SequenceGeometric Sequence

We are given a geometric sequence $\{a_n\}$. We know that $a_4 = 5$. We need to find the value of $a...

SequencesGeometric SequencesSeries

The problem asks to simplify the given expressions and write them in positive index form. This means...

ExponentsSimplificationNegative ExponentsAlgebraic Expressions

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